pg_0025

Process Improvement

5.2.

Assumptions

5.2.4.

Are the model residuals well-behaved.

Residuals are

the

differences

between the

observed and

predicted

responses

Residuals are estimates of experimental error obtained by subtracting the observed responses

from the predicted responses.

The predicted response is calculated from the chosen model, after all the unknown model

parameters have been estimated from the experimental data.

Examining residuals is a key part of all statistical modeling, including DOE's. Carefully looking

at residuals can tell us whether our assumptions are reasonable and our choice of model is

appropriate.

Residuals are

elements of

variation

unexplained

by fitted

model

Residuals can be thought of as elements of variation unexplained by the fitted model. Since this is

a form of error, the same general assumptions apply to the group of residuals that we typically use

for errors in general: one expects them to be (roughly) normal and (approximately) independently

distributed with a mean of 0 and some constant variance.

Assumptions

for residuals

These are the assumptions behind ANOVA and classical regression analysis. This means that an

analyst should expect a regression model to err in predicting a response in a random fashion; the

model should predict values higher than actual and lower than actual with equal probability. In

addition, the level of the error should be independent of when the observation occurred in the

study, or the size of the observation being predicted, or even the factor settings involved in

making the prediction. The overall pattern of the residuals should be similar to the bell-shaped

pattern observed when plotting a histogram of normally distributed data.

We emphasize the use of graphical methods to examine residuals.

Departures

indicate

inadequate

model

Departures from these assumptions usually mean that the residuals contain structure that is not

accounted for in the model. Identifying that structure and adding term(s) representing it to the

original model leads to a better model.

Tests for Residual Normality

Plots for

examining

residuals

Any graph suitable for displaying the distribution of a set of data is suitable for judging the

normality of the distribution of a group of residuals. The three most common types are:

histograms

normal probability plots

, and

dot plots.

5.2.4. Are the model residuals well-behaved.

http://www.itl.nist.gov/div898/handbook/pri/section2/pri24.htm (1 of 10) [5/7/2002 4:01:44 PM]

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